7. Radon Expose in Egyptian Tombs Many ancient Egyptian tombs were cut from limestone rockthat contained uranium. Since most tombs are not well ventilated, guards, tour guides, and visitors maybe exposed to deadly radon gas. In Radiation Protection Dosimetry (December 2010), a study of radonexposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours), was conducted.The radon levels-measured in becquerels per cubic meter (Bq/m³)-in the inner chambers of a sample of15 tombs were determined. Summary statistics follow: 7 = 3, 643 Bq/m3 and s = 4, 487 Bq/m3. For thesafety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombsif the true mean level of radon exposure in the tombs rises to 6,000 Bq/m3. Conduct a test to determineif the true mean level of radon exposure in the tombs is LESS THAN 6,000 Bq/m³, using a Type Ierror probability of 0.05. You may assume that the radon levels in the tombs in the Valley of Kings arenormally distributed. (Complete Parts (a), (b), and (c).)(a) The value of the test statistic (rounded to two decimal places) is(i) -2.03(ii) -1.68(iii) 1.88(iv) -2.41(b) The p-value (rounded to four decimal places) isYou should find one of the following useful for Part (b):P(z < -2.03) 0.0212P(t < -1.68) 0.0576; df = 14P(z < 1.88) 0.9699P(t < 1.88) 0.9595; df = 14P(z < -2.41) 0.0080P(t < -2.03) - 0.0309; df = 14(i) 0.0576(ii) 0.0309(iii) 0.0618(iv) 0.0212(c) Based on your answer to Part (b),(i) Do not recommend that ETA temporarily close the tombs, since there is not sufficient evidencethat the true mean level of radon exposure in the tombs is less than 6,000 Bq/m³.(ii) Recommend that ETA temporarily close the tombs, since there is not sufficient evidence that thetrue mean level of radon exposure in the tombs is less than 6,000 Bq/m3.(iii) Recommend that ETA temporarily close the tombs, since there is sufficient evidence that the truemean level of radon exposure in the tombs is less than 6,000 Bq/m³.(iv) Do not recommend that ETA temporarily close the tombs, since there is sufficient evidence thatthe true mean level of radon exposure in the tombs isthan 6,000 Bq/m³.8

Solution: Given information : n= 15 Sample size x=3643 Sample means= 4487 Sample standard deviations μ=6000 Population meanα=0.05 levvel of significance To test the hypothesis Ho:μ=6000 Vs Ha:μ< 6000 a) Test statistic t=x-μs/nt=3643-60004487/15t= 3643-60004487/3.8729833t=-23571158.5384=-2.0344599t= -2.03 Test statistic t = - 2.03 Option (i) is correct b) To find P value P( t < -2.03) = 0.0309 From excel df= 14 P value = 0.0309 Option (ii) is correct c) Decision: P value < α=0.05 Reject Ho Conclusion: Recommend that ETA temporarily close the tombs since there is sufficient evidence that the true mean level of radon exposure in the tombs is less than 6000 Bq/m^2 Option (iii) is correct .

Math

Statistics

7. Radon Expose in Egyptian Tombs Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well ventilated, guards, tour guides, and visitors may be exposed to deadly radon gas. In Radiation Protection Dosimetry (December 2010), a study of radon exposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours), was conducted. The radon levels measured in becquerels per cubic meter (Bq/m³)-in the inner chambers of a sample of 15 tombs were determined. Summary statistics follow: = 3,643 Bq/m3 and s = 4, 487 Bq/m³. For the safety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombs if the true mean level of radon exposure in the tombs rises to 6,000 Bq/m3. Conduct a test to determine if the true mean level of radon exposure in the tombs is LESS THAN 6,000 Bq/m³, using a Type I error probability of 0.05. You may assume that the radon levels in the tombs in the Valley of Kings are normally distributed. (Complete Parts (a), (b), and (c).)

7. Radon Expose in Egyptian Tombs Many ancient Egyptian tombs were cut from limestone rock that contained uranium. Since most tombs are not well ventilated, guards, tour guides, and visitors may be exposed to deadly radon gas. In Radiation Protection Dosimetry (December 2010), a study of radon exposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours), was conducted. The radon levels measured in becquerels per cubic meter (Bq/m³)-in the inner chambers of a sample of 15 tombs were determined. Summary statistics follow: = 3,643 Bq/m3 and s = 4, 487 Bq/m³. For the safety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombs if the true mean level of radon exposure in the tombs rises to 6,000 Bq/m3. Conduct a test to determine if the true mean level of radon exposure in the tombs is LESS THAN 6,000 Bq/m³, using a Type I error probability of 0.05. You may assume that the radon levels in the tombs in the Valley of Kings are normally distributed. (Complete Parts (a), (b), and (c).)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

7. Radon Expose in Egyptian Tombs Many ancient Egyptian tombs were cut from limestone rock
that contained uranium. Since most tombs are not well ventilated, guards, tour guides, and visitors may
be exposed to deadly radon gas. In Radiation Protection Dosimetry (December 2010), a study of radon
exposure in tombs in the Valley of Kings, Luxor, Egypt (recently opened for public tours), was conducted.
The radon levels-measured in becquerels per cubic meter (Bq/m³)-in the inner chambers of a sample of
15 tombs were determined. Summary statistics follow: 7 = 3, 643 Bq/m3 and s = 4, 487 Bq/m3. For the
safety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombs
if the true mean level of radon exposure in the tombs rises to 6,000 Bq/m3. Conduct a test to determine
if the true mean level of radon exposure in the tombs is LESS THAN 6,000 Bq/m³, using a Type I
error probability of 0.05. You may assume that the radon levels in the tombs in the Valley of Kings are
normally distributed. (Complete Parts (a), (b), and (c).)
(a) The value of the test statistic (rounded to two decimal places) is
(i) -2.03
(ii) -1.68
(iii) 1.88
(iv) -2.41
(b) The p-value (rounded to four decimal places) is
You should find one of the following useful for Part (b):
P(z < -2.03) 0.0212
P(t < -1.68) 0.0576; df = 14
P(z < 1.88) 0.9699
P(t < 1.88) 0.9595; df = 14
P(z < -2.41) 0.0080
P(t < -2.03) - 0.0309; df = 14
(i) 0.0576
(ii) 0.0309
(iii) 0.0618
(iv) 0.0212
(c) Based on your answer to Part (b),
(i) Do not recommend that ETA temporarily close the tombs, since there is not sufficient evidence
that the true mean level of radon exposure in the tombs is less than 6,000 Bq/m³.
(ii) Recommend that ETA temporarily close the tombs, since there is not sufficient evidence that the
true mean level of radon exposure in the tombs is less than 6,000 Bq/m3.
(iii) Recommend that ETA temporarily close the tombs, since there is sufficient evidence that the true
mean level of radon exposure in the tombs is less than 6,000 Bq/m³.
(iv) Do not recommend that ETA temporarily close the tombs, since there is sufficient evidence that
the true mean level of radon exposure in the tombs is
than 6,000 Bq/m³.
8

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